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地理科学  2001 

城市系统的异速生长关系与位序-规模法则——对Steindl模型的修正与发展

, PP. 412-416

Keywords: 城市规模分布,Steindl模型,二倍数规律,Beckmann模型,Zipf定律,对称,分形,复杂性

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Abstract:

基于Steindl模型的建模思想,设置一个时间-年龄变量T,将城市规模(P)-数目(f)异速生长的假设条件重新构造为dP(T)/dT=gP(T),df(T)/dT=-rf(T),据此导出反映城市等级-规模关系的Beckmann-Davis模型P(m)=P1λm-1,f(m)=f1δ1-m,进而导出三参数Zipf定律P(r)=C(r-α)-dz,式中g=lnλ,r=lnδ,C=P1〔δ/(δ-1)〕dz,α=1/(1-δ),dz=g/r=lnλ/lnδ。根据几何测度关系建立分维方程dz=Dp/Df,从而揭示城市规模分布的分维D=1/dz在本质上乃是城市体系空间结构的分维Df与各城市人口空间分布的平均维数Dp之比。

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